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Ordinal data, continuous data, and statistical tests

Several of my clients, and their committee members have had some misunderstandings about the use of parametric statistics with ordinal data, so I decided to write this article.

Many statistical procedures such as Pearson’s correlation and Linear regression analysis require certain assumptions about the data in order for the procedure to be valid. One of those assumptions is regarding the measurement scale of the variables. There are two main types of measurement scales, categorical and continuous. Examples of categorical variables are: 1) gender; 2) what is your favorite color, and; 3) level of agreement, strongly disagree, disagree, neutral, agree, strongly agree. Examples of continuous measurements are: 1) height in inches (measured to the nearest 10th of an inch); weight (measured to the nearest 10th of a pound).

Within categorical measurement scales there are two types, nominal and ordinal. Gender and favorite color are nominal whereas level of agreement is ordinal. The only difference between nominal and ordinal is that the order of the categories for a nominal variable has no meaning whereas an ordinal variable has a meaningful order from smallest to largest. For example, you can’t put favorite color, red, green, blue, yellow in order from least to most, but strongly disagree is clearly less than disagree, which is less than neutral and so on.

It is pretty unusual to have an ordinal dependent variable in research. When ordinal variables are involved in a dependent variable it is far more common to have an instrument consisting of numerous questions, each of which is measured on an ordinal measurement scale. The instrument is designed to produce a scale score, which is an aggregate of the individual survey questions (usually the average of the questions). So, if your survey has 10 Likert-type (i.e. ordinal) questions, you usually aren’t going to be analyzing the individual survey questions themselves. The survey is designed such that you take the average of the 10 questions, which produces a number that can take on fractional values like 1.17, 2.73, 3.47 etc. So, the resultant scale score is the actual measurement (i.e. independent or dependent variable) that you are analyzing, and it is measured on a continuous measurement scale, so it meets that particular requirement of the parametric test, like Pearson’s correlation or linear regression.